Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point M_{c} 50 67.5

color 220 0 0
fontsize 11

cmark_lt H_{c}
cmark_lt M_{c}
color 0 0 0
fontsize 10


% point E_{c} is given by the problem setting, but it has to belong to the line h_{c} which is constructible from the others objects given 
% DET:  points H_{c} and M_{c} are not the same
% Constructing a line c which passes through point H_{c} and point M_{c}
line c H_{c} M_{c} 

color 200 200 200
drawline c
color 0 0 0




% Constructing a line h_{c} which is perpendicular to line c and which passes through point H_{c}
perp h_{c} H_{c} c 

color 200 200 200
drawline h_{c}
color 0 0 0




% Constructing a point P_{\_G41661} with coordinates (10,30)
point P_{\_G41661} 10 30 
cmark_r P_{\_G41661}

% Constructing a line L_{\_G41664} which passes through point M_{c} and point H_{c}
line L_{\_G41664} M_{c} H_{c} 

color 200 200 200
drawline L_{\_G41664}
color 0 0 0


% Constructing a line L_{\_G41667} which is perpendicular to line L_{\_G41664} and which passes through point H_{c}
perp L_{\_G41667} H_{c} L_{\_G41664} 

color 200 200 200
drawline L_{\_G41667}
color 0 0 0


% Constructing a line L_{\_G41670} which passes through point M_{c} and point P_{\_G41661}
line L_{\_G41670} M_{c} P_{\_G41661} 

color 200 200 200
drawline L_{\_G41670}
color 0 0 0


% Constructing a point E_{c} which belongs to line L_{\_G41670} and line L_{\_G41667}
intersec E_{c} L_{\_G41670} L_{\_G41667} 
color 220 0 0
fontsize 11
cmark_r E_{c}
color 0 0 0
fontsize 10



% DET:  points E_{c} and M_{c} are not the same
% Constructing a line m(H_{b}H_{a}) which passes through point E_{c} and point M_{c}
line m(H_{b}H_{a}) E_{c} M_{c} 

color 200 200 200
drawline m(H_{b}H_{a})
color 0 0 0



% DET:  points E_{c} and H_{c} are not the same
% Constructing bisector m(E_{c}H_{c}) of the segment E_{c}H_{c}
med m(E_{c}H_{c}) E_{c} H_{c} 

color 200 200 200
drawline m(E_{c}H_{c})
color 0 0 0

color 200 200 200
drawsegment E_{c} H_{c} 
color 0 0 0


% NDG:  lines m(E_{c}H_{c}) and m(H_{b}H_{a}) are not parallel% DET:  lines m(E_{c}H_{c}) and m(H_{b}H_{a}) are not the same
% Constructing a point N which belongs to line m(E_{c}H_{c}) and line m(H_{b}H_{a})
intersec N m(E_{c}H_{c}) m(H_{b}H_{a}) 
cmark_r N


% NDG:  points E_{c} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point E_{c}
circle k(N,M_{a}) N E_{c} 

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0




% Constructing a point A such that H_{c}A/H_{c}M_{c}=0.013314963663052072
towards A H_{c} M_{c} 0.013314963663052072 
cmark_t A
color 200 200 200
drawsegment H_{c} M_{c} 
color 0 0 0



% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0


% NDG:  points A and M_{c} are not the same
% Constructing a circle k(M_{c},A) whose center is at point M_{c} and which passes through point A
circle k(M_{c},A) M_{c} A 

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  circles k(N,M_{a}) and k(M_{c},A) intersect% DET:  circles k(N,M_{a}) and k(M_{c},A) are not the same
% Constructing points H_{a} and H_{b} which are in intersection of k(N,M_{a}) and k(M_{c},A)
intersec2 H_{a} H_{b} k(N,M_{a}) k(M_{c},A) 
cmark_b H_{a}
cmark_rt H_{b}


% DET:  points A and H_{a} are not the same
% Constructing a line h_{a} which passes through point A and point H_{a}
line h_{a} A H_{a} 

color 200 200 200
drawline h_{a}
color 0 0 0



% NDG:  lines h_{c} and h_{a} are not parallel% DET:  lines h_{c} and h_{a} are not the same
% Constructing a point H which belongs to line h_{c} and line h_{a}
intersec H h_{c} h_{a} 
cmark_rt H



% Constructing a point C such that E_{c}C/E_{c}H=-1
towards C E_{c} H -1 
cmark_b C
color 200 200 200
drawsegment H C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines h_{c} and h_{a} are not parallel; circles k(N,M_{a}) and k(M_{c},A) intersect; points A and M_{c} are not the same; points E_{c} and N are not the same; lines m(E_{c}H_{c}) and m(H_{b}H_{a}) are not parallel
% Determination conditions:  lines h_{c} and h_{a} are not the same; points A and H_{a} are not the same; circles k(N,M_{a}) and k(M_{c},A) are not the same; lines m(E_{c}H_{c}) and m(H_{b}H_{a}) are not the same; points E_{c} and H_{c} are not the same; points E_{c} and M_{c} are not the same; points H_{c} and M_{c} are not the same